PHYSICAL REVIEW B
VOLUME 58, NUMBER 22
1 DECEMBER 1998-II
In-plane flux pinning in melt-textured YBa2Cu3O7-Y2BaCuO5 composites
B. Martı́nez, T. Puig, A. Gou, V. Gomis, S. Piñol, J. Fontcuberta, and X. Obradors
Institut de Ciència de Materials de Barcelona-Consejo Superior de Investigaciones Cientı́ficas,
Campus Universitat Autònoma de Barcelona, Bellaterra 08193 Spain
G. Chouteau
High Magnetic Field Laboratory, 25 Avenue des Martyrs, Boı̂te Postale 166, F-38042 Grenoble Cedex 9, France
~Received 20 April 1998; revised manuscript received 28 July 1998!
The critical currents of a series of YBa2Cu3O7/Y2BaCuO5 ~123-211! melt-textured ceramic composites have
been measured inductively with the field applied parallel to the ab planes (H i ab) and compared to those
previously analyzed when H i c. In-plane vortex pinning mechanisms are analyzed from temperature and field
dependence of J cc (H i ab) in samples with different concentration of 211 particles. A hierarchy of pinning
centers has been identified and analyzed: 123/211 interfaces, dislocations, stacking faults, and twin boundaries.
We show that the interface of the secondary phase Y2BaCuO5 with the superconducting matrix plays an
important role in pinning the Josephson vortices though with a reduced efficiency as compared to Abrikosov
vortices. In addition, we identify a second contribution to flux pinning which is independent of V/d, i.e., the
amount of interface between the Y2BaCuO5 particles and the matrix, that we associate with in-plane linear
defects, such as dislocations and partial dislocations surrounding the stacking faults. Finally, the contribution
to the pinning of Josephson vortices from twin planes has also been evaluated. @S0163-1829~98!03446-8#
I. INTRODUCTION
Melt-textured YBa2Cu3O7/Y2BaCuO5 ~123-211! superconducting composites have been attracting considerable attention since the discovery that, through directional solidification processes,1 the main factor limiting the critical
currents in ceramic superconductors, i.e., high angle grain
boundaries, could be avoided. Under these conditions high
critical currents have been achieved surpassing even those
obtained in 123 single crystals. Any further enhancement of
the critical currents in melt-textured growth ~MTG! superconductors relies on the ability to understand which are the
flux-pinning mechanisms and how they are related to the
microstructure of the ceramic 123/211 composites.2
Investigations of the microstructure of 123/211 MTG
composites by TEM ~Refs. 3 and 4! have evidenced the complexity of these materials where several kinds of defects coexist and interact. Nowadays, a considerable systematic investigation of the formation and evolution of these defects
has been settled and it has been particularly rewarding that
their geometrical arrangement follows clear patterns. It has
been established that the defects which may play a role in the
flux-pinning problem can be classified as: ~1! second phase
precipitates such as 211 particles with a quasispherical geometry, ~2! planar defects lying parallel to the c axis, twin
boundaries for instance, and ~3! linear and planar defects
lying parallel to the ab plane: stacking faults, dislocations,
and microcracks. The knowledge of the detailed structure
and formation mechanisms of these defects enables us now
to analyze one of the most outstanding problems of hightemperature superconductors: their anisotropic behavior.
In a recent work,5 we analyzed systematically the critical
currents of a whole set of samples with different amounts of
211 particles when H i c. There, we demonstrated that the
0163-1829/98/58~22!/15198~10!/$15.00
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123/211 interface plays a dominant role in the pinning behavior of the superconducting composites, but it was also
concluded that secondary defects should not be neglected in
certain regions of the magnetic phase diagram. The collective interaction between vortices was shown to limit the effectiveness of these interfaces in the enhancement of the total
pinning force. The understanding of the anisotropy of the
flux-pinning mechanisms in 123/211 composites is still incomplete and a systematic analysis of the relationship among
the nature of the vortex state in YBa2Cu3O7 ~YBCO! and the
complex microstructure of 123/211 textured ceramics is required.
In layered superconducting cuprates,6 a crossover from
two-dimensional ~2D! to 3D vortex nature occurs when the
Ginzburg-Landau coherence length along the c axis extends
beyond the separation of the CuO2 planes. This crossover
temperature T cr is defined by j c (T cr)5« j ab (T cr)5d/ A2,
where d is the separation among CuO2 planes and « is the
mass anisotropy ratio «5(m ab /m c ) 1/2. At low temperatures
(T,T cr), and depending on the orientation of H with respect
to the CuO2 planes, the usual rectilinear vortex structure
breaks down in a kinked vortex state which consists of pancake vortices with shielding currents lying within the CuO2
planes and vortex strings ~or Josephson vortices! with the
phase core having a dimension d along the c axis and L
5d/« perpendicular to it. This kinked vortex state transforms to a locked state below an angle u L and then B is
strictly parallel to the CuO2 planes. In Y123, T cr can be
estimated as '80 K and hence in most of the temperature
range usually investigated, the 2D nature of the vortices
dominates. In this case depending on the orientation of the
Lorentz force F L , three contributions to bulk pinning must
be distinguished in the kinked state: ~1! pancake pinning
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©1998 The American Physical Society
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IN-PLANE FLUX PINNING IN MELT-TEXTURED . . .
with F L i ab, ~2! intrinsic pinning with F L i c, and ~3! pinning
of vortex strings with F L i ab. The relative relevance of these
three contributions in real systems will strongly depend on
the actual microstructure of the textured ceramics. In this
work, by using the very same samples as in our previous
work,5 we present an accurate analysis of the flux-pinning
mechanisms existing in these materials when the external
magnetic field is applied parallel to the ab planes (H i ab).
The anisotropy of the critical currents in YBCO single
crystals and thin films has already been analyzed by several
authors7 and it has been clearly stated that when the Lorentz
force is perpendicular to the ab planes the critical currents
appear to be largely dominated by the intrinsic pinning
mechanism pointed out by Tachiki and Takahashi8 as a characteristic feature of layered high-temperature superconductors. In the present work, however, we will focus our analysis
on the case when the Lorentz force lies parallel to the ab
plane, i.e., the analysis of the influence of the microstructure
on J cc (H i ab) is our main concern. Actually, the understanding of the behavior of this particular component of the critical current bears strong interest since it is directly related to
the modifications of the microstructure ceramics through
processing treatments and it is not masked by the strong
contribution of the intrinsic pinning. We also note that transport critical current measurements of J cc are very scarce up to
now while it may be easily investigated through magnetization measurements by using the anisotropic Beam model.
We will show that 123/211 interface pinning is still an
effective pinning mechanism in this magnetic-field orientation resembling the correlated disorder behavior observed in
the H i c orientation. Nevertheless, in this case, other defects
not related to 123/211 interface and which we associate with
the linear and planar defects lying parallel to the ab plane
~stacking faults and dislocations! are also of relevance for all
the investigated samples. Finally, we also evaluate the contribution of the twin planes to J cc when H lies parallel to
them. Through a detailed quantification of the pinning contribution of these defects we have been able to infer the
source of the critical current anisotropy in these materials.
II. EXPERIMENT
The preparation and microstructural characterization of
the samples studied in the present investigation has been
largely described in previous works.2,4,9 Essentially, a
Bridgman growth technique has been used to obtain singledomain samples having difference concentration and size of
211 particles. The range of compositions investigated extends from 4 to 38% of 211 in weight and the minimum
mean size reached up to now is about 0.5 mm.2,9 As we
described in our previous work, the actual content of 211
phase in the samples was determined by measurements of
high-temperature paramagnetic susceptibility which displays
a Curie-Weiss law arising from the 211 particles. Only in
this way can a meaningful scaling of the superconducting
properties, with the amount of interface between the 123
matrix and the 211 precipitates, be reached.5 A quantitative
measure of the 123/211 interface may be represented through
the parameter V/d, i.e., the ratio of the volume percentage of
211 phase and the mean diameter of the 211 precipitates
determined by image analysis of SEM photographs.2,9
15 199
The inductive critical currents have been determined from
isothermal and temperature dependent magnetization measurements carried out with a superconducting quantum interference device magnetometer provided with 5.5 T and by
using an extraction magnetometer at the Service National des
Champs Intenses ~Grenoble! of up to 22 T. These measurements were performed on parallepipedic samples of about
231.530.5 mm3. The magnetic field was applied parallel to
the ab plane (H i ab) and out of the $110% twin planes, unless
indicated otherwise, to avoid the contribution of twin boundaries to flux pinning.10–12 The anisotropic Bean model has
been used to compute J cc when the magnetic field is oriented
parallel to one of its edges b, and the direction c is parallel to
the c axis:13
DM 5
J cc a
20
S
12
aJ cc
3cJ ab
c
D
~1!
,
where DM is the irreversible magnetization in Gauss and
a3b3c is the sample volume.
If we take into account that these samples fulfill the conc
dition J cc a!J ab
c c, Eq. ~1! is reduced to J c '20DM /a, a being the larger side of the sample surface perpendicular to the
applied field. Therefore, we can actually determine J cc (H,T),
i.e., the critical current corresponding to a pinning force
pointing parallel to the ab planes when the vortices also remain parallel to the ab planes. It is clear then that no interference with the intrinsic pinning mechanism8 is present in
our measurements. We must also stress that we have indeed
verified that magnetic relaxation effects are not relevant in
most of the investigated regions of the magnetic phase diagram ~except for those very near to the irreversibility line!.
Therefore, our analysis of the field and temperature dependence of J cc is essentially unaffected by flux-creep effects.
The evaluation of the critical current contribution of
twin boundaries was performed in one particular sample
~28% 211 and V/d'2550 cm21! by applying the magnetic
field along $110% planes, within the ab plane, in a sample
with a parallepipedic shape and its edge parallel to the $100%
planes. In this case Eq. ~1! should be generalized to our
particular geometry. After a detailed reconsideration of the
new geometrical features we have obtained the following
generalized equation for a parallepiped a3b3c sample
when the magnetic field is directed at 45° from a and b axis
and the c direction is along the c axis:
DM 5
J cc a
10
F S
12
2J cc a
3 A2cJ ab
c
DG F
2
J cc a 2
30b
J cc a!J ab
c c
12
J cc a
cJ ab
c
G
~ A222 ! .
~2!
Once again the condition
is fulfilled in our
samples and thus Eq. ~2! is reduced to DM 5J cc (a/10
2a 2 /30b) from which we have calculated J cc when the magnetic field is directed along the ^110& directions.
Finally, it is worth mentioning that special care was taken
in the oxygenation process of all our samples. As we have
previously demonstrated,14,15 the duration of the oxygenation
step at 450 ° C is crucial to reach optimum critical currents
because either a deficient layered oxygenation persists when
the process is too short14 or an ageing process appears when
the oxygenation is too long.15 The concomitant microstruc-
B. MARTÍNEZ et al.
15 200
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FIG. 1. Temperature dependence of J cc in textured ceramics
samples with different concentration of 211 phase in self-field conditions. Continuous lines correspond to fits by using the collectivepinning–collective-creep theory @Eq. ~4! in text#. Dashed lines correspond to fits using the correlated disorder pinning theory @Eq. ~3!
in text#.
tural features may strongly affect the observed critical currents anisotropy. The optimum oxygenation treatment for
each sample could be easily monitored by means of low-field
susceptibility measurements with the field parallel to the ab
planes. This was accomplished in all the samples investigated in the present work and so we safely assume that the
measured critical currents are the optimized values for each
composition in what concerns the oxygenation processes.
The critical currents of all the samples, having different
concentration of 211 precipitates, were investigated by determining their temperature dependence at zero external magnetic field, J cc (T), and their field dependence in isothermal
conditions, J cc (H). The experimental procedure for J cc (T) determination was similar to that previously reported when
H i c geometry,5 i.e., the samples were field cooled under a
magnetic field of 5.5 T down to 5 K where the magnetic field
was decreased steadily to zero and then, the magnetization
was measured while the temperature was slowly increased.
Under these conditions the measurements of the persistent
currents were actually performed under self-field conditions
but because we choose carefully the geometry of the samples
this field was never higher than H t 52.5–3 kOe and thus it
had a small influence on the measured critical currents. Isothermal hysteresis loops were used to determine J cc (H).
III. RESULTS
A. Dependence of the critical currents
on the Y2BaCuO5 concentration
Figure 1 shows the temperature dependence of J cc measured in self-field conditions in several samples with different concentration of 211 phase. First of all, it should be noted
that there is a clear correlation between the critical currents
and the amount of 211 phase in the sample. Similarly to the
H i c case,5 this suggests that 123/211 interface pinning
mechanism plays an important role at low fields. On the
other hand, the temperature dependences of Fig. 1 reveal a
softening above T'40 K. This softening appears to be a
phenomenon typical of melt-textured 123/211 composites.
Measurements of critical currents for H i c in the same
FIG. 2. Dependence on the 123/211 interface specific area of ~a!
the nonrelaxed critical currents J 0c and J 00 included in Eqs. ~3! and
~5!, respectively, and ~b! the pinning energy terms T * and U 00
included in Eqs. ~3! and ~6!, respectively. All the data correspond to
measurements performed in self-field conditions.
samples here studied,5 indicated that this softening could
arise from a change in the dominating pinning centers. It was
already suggested there that, 123/211 interfaces might have
an enhanced contribution to flux pinning at high temperatures, because thermal activation enables the wandering of
the vortex lines. Thus, depinning from the weaker pinning
centers and bending is induced and vortices might be able to
take as much advantage of 123/211 interface pinning as possible. Under those circumstances, the flux-line lattice is able
to adjust itself to the random distribution of the 123/211
interfaces, resembling the behavior theoretically described
by Nelson and Vinokur16 as correlated disorder pinning and
which typically occurs in ion-irradiated single-crystalline
superconductors.17,18 The occurrence of a similar phenomenon for the present field orientation (H i ab) is very likely.
The equation describing this pinning regime, when the concentration of vortices is below the so-called matching field,
is given by the following expression:
J cc ~ T ! 5J 0c exp23 ~ T/T * ! 2 .
~3!
This fits by using this correlated disorderlike expression
are indicated by dashed lines in Fig. 1. It is observed that this
law reproduces nicely the experimental results in the temperature range 40 K<T<75 K, in close correspondence with
the behavior observed in the H i c geometry.
Figures 2~a! and 2~b! show the dependence of the two
IN-PLANE FLUX PINNING IN MELT-TEXTURED . . .
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15 201
fitting parameters of Eq. ~3!, J 0c and T * on the 123/211 interface specific area measured through the parameter V/d,
where V is the volume percentage of 211 phase and d is the
mean diameter of the 211 precipitates. The existence of a
clear correlation between the parameters characterizing the
strength of the 123/211 interface pinning, i.e., J 0c and T * ,
and the interface specific area is evident. The linear relationship observed gives further support to the idea that 123/211
interfaces contribute to pinning in this field orientation where
the Lorentz force is parallel to ab planes. We note, however,
that the J 0c values do not extrapolate to zero when V/d goes
to zero, as it was the case for the H i c geometry. This fact
indicates that additional pinning contributions which are independent of the V/d parameter, should be considered. As
will be discussed later, microstructural defects lying parallel
to ab planes like in-plane dislocations, 1/6@301# partial dislocations surrounding stacking faults and in-plane lines surrounding the microcracks parallel to ab planes2,4,19 might be
good candidates.
At temperatures below '40 K, the critical currents do not
follow the behavior predicted for correlated disorder @Eq.
~3!#. Instead, experimental results are better described by the
law expected for collective-pinning—collective-creep
theory20
J cc ~ T ! 5
J c0
.
@ 11 ~ m T/U 0 ! ln~ t/t eff!#
~4!
In a similar way to the procedure used in YBa2Cu3O7
single crystals21 and melt-textured ceramics5 in the H i c geometry, phenomenological laws for the temperature dependence of J c0 and U 0 can be used in Eq. ~4!. These laws are
the following:
F S DG
,
F S DG
.
J c0 ~ T ! 5J 00 12
U 0 ~ T ! 5U 00 12
T
Tc
T
Tc
2 n
~5!
2 n
~6!
These expressions are derived from the BCS temperaturedependent coherence length and the thermodynamic critical
field. In order to minimize the number of fitting parameters,
all the constants were fixed to those previously used in the
H i c field orientation,5 i.e., ln (t/teff)>33 and n53/2. In this
way the unique fitting parameters are the nonrelaxed critical
current J 00 and the pinning energy barrier at 0 K U 00 .
The reason for the experimental agreement with these
laws may arise from the fact that, when the temperature is
lowered, thermal activation decreases and different pinning
centers might become active in these melt-textured ceramics
with such a rich microstructure. We should expect a coexistence of weak and strong pinning centers and thus the scenario may be more akin to that described by the collectivepinning theory. Instead, at high temperatures, only the
strongest centers will remain active and a collective pinning
theory will not be able to describe the experimental results.
FIG. 3. Magnetization hysteresis loops measured at different
temperatures with the magnetic-field-oriented H i ab. All the measurements correspond to a sample with 30% of the 211 phase and
V/d'3451 cm21.
Figures 2~a! and 2~b! show that the J 00 and U 00 dependence on the V/d parameter. An overall increase of both J 00
and U 00 with the amount of 123/211 interface is observed,
and similarly to the case of H i c orientation, the experimental
points are more scattered than those corresponding to the
correlated disorder pinning, i.e., J 0c and T * . This suggests
that the weak pinning centers, also contributing to pinning in
this low-temperature region, are affected by a highest degree
of randomness between the different samples that the strong
pinning centers dominating at high temperatures. It is interesting to note that the maximum J cc values observed in our
melt-textured samples approach those observed in untwined
a-axis-oriented thin films.7
Figures 3~a! and 3~b! display typical isothermal hysteresis
loops from which the field dependence of the critical currents
has been evaluated. The corresponding critical currents are
shown in a log-log plot in Figs. 4~a! and 4~b!. From these
plots it may be noted that in most of the investigated regions
of the magnetic phase diagram, the field-dependent critical
current density may be described by a power law J cc
' b c H 2 a . In addition and similarly to the temperaturedependent critical current measurements reported in Fig. 1,
we observe an increase of J cc with the concentration of 211
particles. This gives further support to the idea that 123/211
interfaces do act as pinning centers in these melt-textured
samples.
The temperature dependence of the power-law exponent
of J cc (H), a, is depicted in Fig. 5 for two representative
15 202
B. MARTÍNEZ et al.
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FIG. 6. Temperature dependence of the self-field critical currents J cc (T) measured with the field orientations H i ^ 100& and
H i ^ 110& . Both measurements correspond to the same sample with
28% 211.
FIG. 4. ~a! and ~b! Field dependence of the inductive critical
amounts J cc as calculated from the experimental hysteresis loops,
assuming the validity of the anisotropic critical-state model. The
continuous lines correspond to fits where a power-law dependence
J cc }H 2 a is found to be valid. All the data correspond to the sample
with 30% 211 and V/d'3451 cm21.
samples. Note that while at low temperatures a'0.3, similarly to the value observed in the H i c orientation for melttextured 123/211 composites5 and 123 epitaxial thin films,22
at higher temperatures and up to T'70 K a plateau is observed around a'0.5. Above 70 K, this exponent suddenly
increases towards a'1.0, the coefficient typically observed
in the single vortex pinning regime by point defects.23
B. Twin boundary influence on the critical currents
28% 211 with V/d'2550 cm21, through a comparison of
the temperature and field dependence of the critical currents
when H i ^ 110& and H i ^ 100& . In Fig. 6 we compare the temperature dependence of J cc (T) for those two particular field
orientations. The calculation of J cc for H i ^ 110& has been performed following the extended critical-state analysis indicated before. Figure 6 also shows the fits corresponding to
correlated disorder pinning @Eq. ~3!# for both field orientations. As appreciated clearly, for H parallel to the twin planes
J cc is higher than for H i ^ 100& for all the temperature range
except for temperatures approaching T c .
Figure 7 shows the field dependence of J cc (H) at different
temperatures for the two orientations mentioned above and,
once again, we can signal a clear enhancement of J cc when
H i ^ 110& . A J cc ' b c H 2 a law may here also be applied. Furthermore, when the temperature dependence of the coefficient a is analyzed for H i ^ 110& , a behavior similar to that
represented in Fig. 5 is also found. We may then conclude
that twin boundaries ~TB’s! are indeed effective defects for
in-plane flux pinning when the Lorentz force remains parallel to the ab planes, in agreement with earlier analysis.11
The analysis of the influence of twin planes on the critical
currents for H i ab was carried out in one particular sample,
FIG. 5. Temperature dependence of the power-law coefficient a
representing the field dependence of the critical currents J cc }H 2 a .
The data correspond to samples with 211 additions of 30 and 20%.
FIG. 7. Magneto-field dependence of the critical currents measured in a sample with 28% 211, at the temperatures indicated and
with the magnetic field oriented along ^100& and ^110& directions.
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IN-PLANE FLUX PINNING IN MELT-TEXTURED . . .
FIG. 8. Field dependence of the J cc critical currents measured at
60 and 77 K together with the fits by using a power-law dependence. It should be noted that a single law can reproduce all the
examined magnetic-field range. The data correspond to a sample
with 20% 211.
IV. DISCUSSION
A. Flux-pinning defects
In the previous paragraph we have conclusively shown
that there is a correlation between the critical current of 123/
211 melt-textured composites and the amount of 211 precipitates distributed in the 123 matrix and we have associated
this correlation to interface pinning.
It was suggested by Murakami et al.24 that the interface of
211 precipitates in melt-textured 123 superconductors may
become active pinning centers through a core-pinning
mechanism. Within this approximation, the field dependence
c
of J ab
c (H) and J c (H) may be described by the laws
J cc 5
J ab
c 5
pj c B 2c N p d 2
1/2
4 m 0 f 1/2
0 B
pj ab B 2c N p d 2
1/2
4 m 0 f 1/2
0 B
5 b c B 21/2,
~7!
5 b ab B 21/2,
~8!
where N p is the number of 211 inclusions per unit volume
and d is their mean size. Thus, J c is proportional to N p d 2 ,
which corresponds to the quantity V/d, V5N p d 2 being the
volume fraction of the 211 precipitates. Note that the value
observed for the coefficient a in the plateau regime of the
field-dependent critical current of Fig. 5 was a;0.5, in
agreement with Eq. ~7!. This agreement is further evidenced
in Fig. 8 where the value of a50.5 was directly imposed to
the experimental data. Notice that for this magnetic-field orientation (H i ab), the field dependence of J cc (H) is indeed
well represented by the same coefficient a50.5 of Eq. ~7! up
to 5 T.
Furthermore, Eq. ~7! predicts that the b c coefficient varies
linearly with the V/d parameter and this is, indeed, what is
observed in Fig. 9. However, Fig. 9 identifies again a background contribution to b c , in close similarity to what was
also found in Fig. 2~a! for the J c0
c term. Therefore, the results
reported so far indicate that when H i ab, both the temperature and field dependence of J cc , have simultaneously a con-
15 203
FIG. 9. Dependence on the 123/211 interface specific area V/d
of the proportionality parameter b c in the power-law field dependence of the critical currents represented by Eq. ~7! in the text.
tribution arising from 123/211 interfaces and a background
contribution not related to the 123/211 precipitates.
Consequently we may write the following generalized expressions for J cc where both contributions are considered:
J cc ~ H ! 5 ~ b cb 1 b cI ! H 2a 5 @ b cb 1 b c0 ~ V/d !# H 2a ,
~9!
0I
2
J cc ~ T ! 5 @~ J 0b
c 1J c !# exp23 ~ T/T * !
c
2
5 $ @ J 0b
c 1A ~ V/d !# % exp23 ~ T/T * ! ,
~10!
cb
correspond to the background values and
where J 0b
c and b
c
c0
A and b are the slopes of the straight lines observed in
Figs. 2~a! and 9, respectively, and hence all these parameters
are independent of the interface parameter V/d. Note that
both the background and the interface contribution are of the
same order of magnitude, i.e., if we look at the zero-field
contribution of J cc , as determined from the correlated disorder pinning fits @Eq. ~10!#. The maximum contribution to J cc
4
2
due to 123/211 interfaces is J 0I
c '5310 A/cm , while the
0b
background value amounts J c '23104 A/cm 2.
Now, having established that two different source of flux
pinning exist in 123/211 composites when the vortices lie
along the ab planes, the issue is to identify the defects responsible for the second identified mechanism, i.e., the background contribution. To answer this question the fact that the
corresponding defects should have a field-dependent contribution to J cc similar to that of the 123/211 interfaces, since a
unique J cc ' b H 2 a law holds over all the investigated field
range, should be taken into account. This actually restricts
the nature of defects to be considered. Furthermore,
this background contribution was not observed in the H i c
configuration. Thus, it is very likely that the corresponding
defects will be linear and planar defects confined in the ab
planes. The main candidates to become effective pinning
centers when H i ab and F L i ab, are the in-plane dislocations
and 1/6@301# partial dislocations surrounding the stacking
faults, if we do not consider for the moment the twin
boundaries.2,4,19 All these defects have been systematically
observed by TEM in 123/211 composites in large numbers
so that they might account for the non-negligible background
contribution observed.
In addition, the in-plane linear defects lying parallel to the
ab planes have shown to have a tendency to be directed
15 204
B. MARTÍNEZ et al.
along the $100% direction.2 In the case of dislocations, the
main reason seems to be the elastic interaction with preexisting defects such as twin boundaries.25 For partial dislocations, it has been experimentally observed that the growth of
stacking faults during the low-temperature oxygenation process is anisotropic and in the form of long fingerlike
figures.2,15,19 In both cases, fragments of vortices might become pinned in short segments at the core of the linear defects showing a behavior J cc }B 21/2.23,26 In-plane dislocations
and stacking faults have been already considered as potential
flux-pinning candidates in 123/211 ceramics even when
H i c.27–29
We may now extend our analysis of the temperature and
field dependence of the critical current J cc to the case where
twin boundaries are considered as well. A new term arising
from twin boundary pinning should be included in Eqs. ~9!
and ~10!:
J cc ~ H ! 5 @ B cb 1 b cI 1 b cTB# H 2 a ,
~11!
0I
0TB
2
J cc ~ H ! 5 @~ J 0b
c 1J c 1J c !@ exp~ 3 ~ 2T/T * ! # ,
~12!
where the J 0TB
c Þ0 only when H is oriented along $110% and
T * is assumed to be similar for the different microstructural
defects. The effectiveness of TB’s as a defect array leading
to a Bose glass phase was already pointed out by Nelson and
Vinokur16 and experimentally verified, through anisotropic
magnetoresistance,10 anisotropic magnetization11 and direct
transport critical current measurements of J cc at 77 K.12
A quantification of the different contributions to Eq. ~12!
gives the following values ~see Figs. 2 and 6!:
4
2
4
2
J 0b
J 0I
and J 0TB
c '2310 A/cm ,
c '3310 A/cm
c
'1.53104 A/cm2 for the sample with V/d'2550 cm21
which indicates an increase of J 0c by twin boundaries of 30%.
Therefore, we confirm that in the low-field single vortex pinning limit the three terms contribute to pin vortices but with
an hierarchy between them.
A similar conclusion may be drawn comparing the b coefficients @Eq. ~11!# describing the field dependence of the
critical currents of the sample with 28% of 211 phase. In this
case, an enhancement of J c '40% ~see Fig. 7!, independently of the temperature, has been found. However, it
should be mentioned that on approaching the irreversibility
line an enhanced divergence among the different critical currents appears, thus suggesting that the irreversibility line
could strongly differ for $100% and $110% orientations, in
agreement with the results reported by Sanfilippo et al.12
It is worth signaling that no traces of field saturation of
J cc (H) below the nominal matching field of the twin boundary array of planes, B * '0.6 T,12 which corresponds to a
mean separation between TB planes of about 1.000 Å, are
observed. This is indeed the mean separation value observed
in our TEM analysis of the present 123/211 ceramics.4 In
spite of that, J cc (H) increases continuously below H * at all
investigated temperatures. Similar results have been found
by other authors from inductive critical current
measurements.11 We should note at this stage that H * remains well above the self-field H t of our samples at 77 K and
that J cc (H) do not show any modification of the field dependence on crossing H * . In conclusion, evidences of flux pin-
PRB 58
ning of Josephson vortices at TB planes in 123/211 composites are given, but with a limited efficiency as compared to
other existing defects.
B. Anisotropy of critical currents
We have shown that the critical currents for H i ab, J cc ,
are about one order of magnitude smaller than the ones obtained for H i c, J ab
c ~Ref. 5! for 123/211 melt-textured material, though this depends, among other factors, on the V/d
value of the specific sample. In order to study the anisotropy
of J c , one might initially just determine the ratio between
c
the two experimental J c ’s, i.e., J ab
c /J c . However, this ratio
will account for the intrinsic anisotropy of the material, the
different nature of the vortices ~i.e., Josephson or Abrikosov!
and also for the different microstructural defect contributions
on J cc and J ab
c and their corresponding field dependences.
This will result in a very complex analysis of the anisotropy.
In the following, we will analyze separately the different
contributions.
Initially we will try to infer on the nature of the anisotropy of the material, previously to the consideration of the
anisotropic nature of the microstructural defects. In this case,
we define an anisotropy ratio by dividing the two slopes A ab
and A c of the linear relationship between J 0c and V/d @see
Fig. 2~a! and Eq. ~10!#. This anisotropy ratio, A ab /A c is independent of the linear and planar defects and it should only
account for the intrinsic anisotropy of the material or the
different nature of the vortices generated when H i c or H i ab
~Abrikosov or Josephson, respectively! if spherical 211 particles are assumed. Figure 10~a! shows the J 0c (V/d) dependence for the two cases, H i ab and H i c, from which the
values A ab 5203 A/cm and A c 514.5 A/cm have been determined. Therefore, the anisotropic ratio is A ab /A c '14. This
is twice the expected value ( j ab / j c '7), assuming that anisotropic Abrikosov vortices become pinned by a d T c core
pinning mechanism at the 123/211 interfaces, as described
by Eqs. ~7! and ~8!.23,24 We note that this ratio could be even
greater if we consider that the actual concentration of inplane defects could slightly increase with V/d and thus the
real contribution from the 211 interfaces when H i ab would
be correspondingly smaller. It is worth it to emphasize, however, that the anisotropy ratios deduced from our analysis
are very similar to those reported by Kuhn et al.30
after magneto-optic flux penetration measurements in
similar melt-texture 123/211 ceramics. Single-crystalline
YBa2Cu3O7 samples display much higher critical current anc
i
i
isotropy ratios @ J ab
c (H c)/J c (H ab)'68 ~Ref. 31!#, thus
indicating that completely different pinning mechanisms
hold in both cases.
This seems to indicate then that the coreless Josephson
vortices are actually less effectively pinned than the
Abrikosov vortices. A similar conclusion for point pinning
centers was recently drawn by Berghuis et al.7 in their study
of the anisotropy of J c in thin films grown over vicinal substrates, where a clear separation of the contribution to pinning from pancake and Josephson vortices was achieved.
Furthermore, the expectation of a reduced efficiency for
single-vortex pinning of a Josephson vortex, as compared to
Abrikosov vortices, was already theoretically discussed by
Blatter et al.6
PRB 58
IN-PLANE FLUX PINNING IN MELT-TEXTURED . . .
15 205
and L pk is the total pancake length. Thus, since L pk /L st
'tan(Du/2), the ratio of the two pinning forces will be given
by
f pk
p
J pk
c sin~ D u !
fp
J stc
st 5
FIG. 10. ~a! Dependence on the 123/211 interface specific area
V/d of J 0c for H i c and J 0c for H i ab magnetic-field orientations. ~b!
Ratios J 0c (H i c)/J 0c (H i ab) as a function of the 123/211 interface
specific area.
Additionally, we should consider when deducing the pinning efficiency of the Josephson vortices from the anisotropy
ratio described above, and specially for the case of melttextured composites, the influence of the mosaic structure
inherent to these ceramics. X-ray rocking curves of ~001!
reflections in 123/211 ceramics grown by Bridgman usually
display a full width at half maximum Du'2–3°.2,9 Therefore, it is necessary to estimate how this misorientation influences our previous assessment. The vortex structure of
melt-textured materials, when the magnetic field is intended
to be directed along the ab planes and when T,T cr , the
crossover temperature from a 2D to a 3D vortex nature, will
always consist of a kinked configuration with some residual
pancakes associated with the magnetic-field component parallel to the c axis and some segments of Josephson vortices
~strings! directed along the ab planes.6,7 We will show that
even in this case, the pinning force contribution from the
Abrikosov pancakes is very small in comparison with that of
the Josephson strings, and therefore that the main contribution to the kinked vortex will come from the Josephson
string segments. The pinning force associated with the segments of Josephson strings might be defined as f st
'J stc •L st , where J stc is determined at the magnetic field H
5H cos(Du/2), and where ~Du/2! is the average misalignment of the magnetic field and the ab planes and L st is the
total string length. Similarly, the pinning force associated
with the pancake vortex segments might be given by f st
pk
'J pk
c •L st , where now J c is determined at H5H sin(Du/2)
.
~13!
Using the J c experimental values obtained in our samples for
3 T,H,5 T and 40 K,T,70 K and Du'2–3°, a value of
st
f pk
p / f p '0.1 is estimated. This confirms that the main contribution to the J cc values previously calculated through the
Beam model, arises mainly from Josephson vortices. Then, it
can be concluded that our results also seem to indicate that
Josephson vortices exhibit a reduced pinning efficiency in
comparison to what should be expected from an anisotropic
Abrikosov vortex in agreement with Refs. 6 and 7.
As a last remark we should also comment on the origin of
the sudden increase of the power-law coefficient a when
increasing temperature ~Fig. 5!. As mentioned before, the
vortex structure of YBa2Cu 3O7 displays a 2D-3D transition
at T cr'80 K when the condition j c 5d/ A2 is fulfilled. It is
then tempting to interpret that when the low-temperature
kinked vortices become again linear at T.T cr the effectiveness of the pinning mechanisms described above break down
and a behavior more akin to that observed in materials with
point defects becomes effective, thus leading at low fields in
the single vortex pinning regime to a power-law field dependence with a'1.23 Additionally, at these high temperatures a
new behavior is evidenced characterized by a faster field
dependence of J cc @Fig. 4~b!#. This probably indicates a crossover to a collective-pinning regime when approaching the
irreversibility line.
Finally, we close by discussing the real meaning of deterc
mining the anisotropy of the critical currents, J ab
c /J c in melttextured 123/211 superconductors. We have shown that
mainly two contributions can be ascribed to J cc , the 123/211
isotropic interface pinning and the background associated
with anisotropic linear and planar defects. Instead, only one
5
contribution was assigned to J ab
c at low fields: the isotropic
interface pinning. This indicates that in general the ratio
c
J ab
c /J c is influenced by the morphological anisotropy of the
linear and planar defects, by the intrinsic anisotropy of vortices in YBa2Cu3O7 and by their corresponding field and
temperature dependences. In particular in Fig. 10~b! we display the zero-field ratio J 0c (H i c)/J 0c (H i ab) as a function of
V/d which according to Eq. ~3! is temperature independent.
As it may be observed this ratio increases with V/d. At large
values of interface area V/d the influence of linear in-plane
defects is minimized, whereas the opposite occurs in the
limit of small V/d values. In the former case, the ratio
J 0c (H i c)/J 0c (H i ab) will reflect mainly the intrinsic nature of
vortices pinned at the interface and it should extrapolate to
J 0c (H i c)/J 0c (H i ab)'14, owing to the observed ratio of the
slopes in Fig. 10~a!.
V. CONCLUSIONS
The main objective of our experimental investigation was
to analyze the sources of the anisotropic pinning in melttextured 123/211 composites and to relate them to the ob-
15 206
B. MARTÍNEZ et al.
served microstructure. Particularly, it was very appealing to
elucidate if the intrinsic differential nature of the vortices
when H i ab, which must be described in terms of Josephson
strings, leads also to a different behavior concerning flux
pinning by defects.
A careful analysis of the temperature and field dependence of the critical currents, as a function of the amount of
123/211 interface, has evidenced in a consistent way that
Josephson strings are pinned both by the precipitates and by
additional in-plane linear defects. The relative contribution
of the latter, however, is progressively reduced when the
concentration of 211 precipitates is increased. At our maximum doping level the single vortex pinning contribution
arising from the interface is 250% higher than that associated
to the linear defects such as dislocations and partial dislocations surrounding the stacking faults.
The effectiveness of the interface pinning mechanism for
Josephson strings has been also evaluated. It has been found
that the pinning energy of a Josephson vortex is reduced by
about 50% as compared to that expected for an anisotropic
Abrikosov vortex when core pinning is considered. A similar
reduction ratio for point defects in thin films has been recently reported7 and was previously postulated theoretically
by Blatter et al.6
Within this context the anisotropy of the low-field critical
currents has been shown to depend strongly on the concentration of 211 particles and it is actually a reflection of the
balance between two different terms: ~1! Flux pinning by
in-plane defects like dislocations and partial dislocations
which are active for all the compositions of melt-textured
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PRB 58
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observation of modified anisotropy ratios must be taken with
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Finally, we have also estimated, for a particular composition, the contribution of twin boundary planes to pin coreless
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ACKNOWLEDGMENTS
The research reported in this work has been supported by
CICYT ~MAT95-0742!, Programa MIDAS ~Red Eléctrica de
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Scientific Facilities. T. P. wishes to thank Ministerio de Educación y Cultura for financial support.
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24